Progress in Fractional Differentiation & Applications

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In this article, a fractional model of HIV/AIDS that includes treatment and a time delay is investigated. The global dynamics of the spread of the disease are discussed using the reproduction number. There is no infected equilibrium if R0 ≤ 1. We also show that the equilibrium point E1 is globally asymptotically stable (the disease disappear). When R0 > 1, there is a unique infected point E2. We introduce sufficient conditions for the stability of E2. Sufficient conditions are given to guarantee the asymptotic stability of the equilibria independent of time delay. We present threshold values of the time delay that the treatment will be succeeded if its positive effects appear before this values. A finite difference method for a general fractional system is presented and is used in the numerical simulations of the model.

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